Problem: What do the following two equations represent? $-5x+5y = 1$ $-25x+25y = -4$
Solution: Putting the first equation in $y = mx + b$ form gives: $-5x+5y = 1$ $5y = 5x+1$ $y = 1x + \dfrac{1}{5}$ Putting the second equation in $y = mx + b$ form gives: $-25x+25y = -4$ $25y = 25x-4$ $y = 1x - \dfrac{4}{25}$ The slopes are equal, and the y-intercepts are different, so the lines are parallel.